Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int a[103][103], l[103], b[103][103], r[103];
int main() {
  int n, m, sum = 0, ans = 0, ans2 = 0;
  scanf("%d%d", &n, &m);
  memset(l, 0x3f, sizeof(l));
  memset(r, 0x3f, sizeof(r));
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= m; ++j) {
      scanf("%d", &a[i][j]);
      b[j][i] = a[i][j];
      sum += a[i][j];
      r[j] = min(r[j], b[j][i]);
      l[i] = min(l[i], a[i][j]);
    }
  }
  for (int i = 1; i <= n; ++i) {
    sum -= l[i] * m;
    ans += l[i];
    for (int j = 1; j <= m; ++j) {
      a[i][j] -= l[i];
    }
  }
  for (int i = 1; i <= m; ++i) {
    ans2 += r[i];
    for (int j = 1; j <= n; ++j) {
      b[i][j] -= r[i];
    }
  }
  for (int i = 1; i <= m; ++i) {
    if (a[1][i] != 0) {
      for (int j = 2; j <= n; ++j)
        if (a[j][i] != a[j - 1][i]) return 0 * puts("-1");
      ans += a[1][i];
      sum -= a[1][i] * n;
    }
  }
  for (int i = 1; i <= n; ++i)
    if (b[1][i] != 0) ans2 += b[1][i];
  if (sum) return 0 * puts("-1");
  if (ans <= ans2) {
    printf("%d\n", ans);
    for (int i = 1; i <= n; ++i)
      for (int j = 1; j <= l[i]; ++j) printf("row %d\n", i);
    for (int i = 1; i <= m; ++i)
      for (int j = 1; j <= a[1][i]; ++j) printf("col %d\n", i);
  } else {
    printf("%d\n", ans2);
    for (int i = 1; i <= m; ++i)
      for (int j = 1; j <= r[i]; ++j) printf("col %d\n", i);
    for (int i = 1; i <= n; ++i)
      for (int j = 1; j <= b[1][i]; ++j) printf("row %d\n", i);
  }
  return 0;
}